Francis Seaman is Professor of Philosophy at the University of Idaho, Moscow, Idaho.
The following article appeared in Process Studies, pp. 129-133, Vol. 5, Number 2, Summer, 1975. Process Studies is published quarterly by the Center for Process Studies, 1325 N. College Ave., Claremont, CA 91711. Used by permission. This material was prepared for Religion Online by Ted and Winnie Brock.
Einstein’s formation of the theory of relativity states that the geometry of the world is variable, its metric being a function of gravitational and electromagnetic field variables. Whitehead disagreed: Our knowledge of nature requires the uniformity of the spatial-temporal continuum which is a continuum of overlapping events, some of which are indefinitely large.
The relationship between Whitehead’s concept of God and traditional religious and theological views has been much discussed, but the relationship between his account of God and his conception of the foundations of science has not. Briefly, Whitehead initially (in works published circa 1919-1924) objected to Einstein’s formulation of the theory of relativity on the grounds that for Einstein the geometry of the world was variable, its metric being a function of gravitational and electromagnetic field variables. But, Whitehead argued, this could not be so, since our knowledge of nature required the uniformity of the spatial-temporal continuum which he characterized as a continuum of overlapping events, some of which were indefinitely large. Nature, he said in these works, was that which was given to mind. He declined to consider any synthesis between mind and nature, calling such a synthesis a venture into metaphysics.
In Process and Reality, Whitehead gave up his account of the spatial-temporal as a continuum of overlapping events in favor of an account of atomic occasions which were distinct and which succeeded one another endlessly. In so doing, Whitehead felt a need to provide for the uniformity of the spatial-temporal in which he had earlier located the basis of that uniformity essential for our knowledge of nature. This ultimate ground of uniformity he found in the antecedent nature of God. In broad outlines, the development of this feature of Whitehead’s thought derived from his work on Principia Mathematica.
The dominant view of the nature of mathematics at the time of the writing of the Principia was (and still is) Formalism. According to this view, mathematical systems are deductions from arbitrarily asserted (postulated) axioms and definitions. In Principia Mathematica, on the other hand, beginning with a few primitive propositions, the authors undertook to show that all the inferences in mathematics could be made with the logical apparatus there developed. In arguing against the Formalist view, Russell once observed that postulating what could be deduced had all the advantages of theft over honest labor.
Further, while formal mathematical systems may or may not be interpreted, i.e., their expressions may or may not be correlated to the world, Principia Mathematica. was throughout an interpreted system. Indeed, numbers themselves were defined by reference to the world (cf. sum., sec. A, vol. 2). Three volumes of this work were published, and according to Russell, Whitehead had done some work on a fourth volume, the design of which was to extend the work of the previous volumes to geometry. In that volume, given the character of the Principia, one may assume that projective geometry would have been developed first, and then geometry as most people know it, involving propositions about comparative lengths and about congruence of various figures, would have been deduced. Geometry, so developed, would have provided the basis for measurement, and measurement, in turn, was the basis for physical science. Such at least are the main steps of the sketch Whitehead gives of this subject in part 4 of Process and Reality.
However, according to the theory of relativity, verified in 1919, the geometry of the world was a variable, being itself a function of gravitational and electromagnetic field variables. For Whitehead, the idea that measurements could lead physicists to a theory which required modification of the geometry which constituted the basis for these measurements seemed incoherent. Indeed, Whitehead contended, for measurements in different regions of the world to be meaningfully related, and for physical theory to be so verified, the geometry of the world had to be uniform. He wrote, "I cannot understand what meaning can be assigned to the distance of the sun from Sirius if the very nature of space depends upon causal intervening objects which we know nothing about" (R 58). Thus, in a series of works published in 1919 and the early 1920s, in opposition to relativity theory, Whitehead argued not only that the geometry of the world was uniform, but that "the properties of time and space express the basis of the uniformity in nature which is essential for our knowledge of nature as a coherent system" (R 8, 29).1 Furthermore, he held that this uniformity was actually discerned there (H 14).
These views did attract attention and had an initial plausibility. As mathematical physicists well knew, in order to use such mathematical processes as differentiation, it is necessary to have a coordinate system. But if, as Einstein held, the metric of the world is variable, the question as to how to institute the requisite coordinates was clearly significant. One strategy was to develop the needed coordinate system by means of tangent flats. Since these flats presumably would be Euclidean in character, the view that an Euclidean, or at least a uniform space, did exist in which gravitational and electromagnetic fields did act seemed plausible. Also, Whitehead’s formulation was a kind of action-at-a-distance theory and so, congenial to traditionalists.
However, his reformulation of relativity was not accepted by physicists, no doubt because he was never able to show any confirmable difference between the predictions of observable fact derived from his theory and that of Einstein. Indeed, Eddington was able to show that Whitehead’s formula for the track of a particle in a gravitational field was exactly equal to that given by Einstein’s equations (Nature, 1924, p. 113). Given that there was no verifiable difference between the two theories, physicists normally prefer the way of discovery. In this case, the tendency to do so was reinforced by a conviction that Whitehead’s account was ad hoc, while Einstein’s account had a beauty and a natural development which carried conviction. While orthodox relativity theories did grant the need to use tangent flats, or an equivalent, in instituting coordinates into the variable space of relativity, they held that these flats were mere scaffolding and not a part of reality. Hence, Whitehead’s work did not deflect the development of modern physics.
Ironically, it was Whitehead’s own work which induced Russell, his co-author of Principia Mathematica, not to go along with him on these matters. As is well known, the method of Newton’s Philosopiae Naturalis Principia Mathematica, after which Russell and Whitehead’s work was modeled, was to infer particular propositions from phenomena and then render these general by induction. According to Russell, it was Whitehead who persuaded him to substitute logical constructions composed of events for the smooth logical properties of mathematical physics, such as points of space, instants of time, and particles of matter. (Cf. Principles of Mathematics, Preface to the Second Edition, p. xi.) So successful was this approach that Russell, as well as the Positivists, perceived no problem in relating the observed properties of the world to any logically consistent physical theory. But Whitehead, more imbued with the Newtonian spirit of generalizing from primitives to a complete physical theory, considered that it was a mistake, indeed, it was incoherent, to begin with measurements based on a particular geometry and construct a theory of the world which required the adoption of a different geometry.
At this stage, Whitehead regarded himself as writing on physics, or rather natural philosophy, in the traditional sense of that latter phase. For example, he stated in the Concept of Nature, that Nature presented itself to the mind as a closed or a self-contained system. "We leave to metaphysics the synthesis of the knower and the known" (CN 28; cf. PNK vii). When Whitehead came to America, he took up the challenge of that synthesis.
In his writings in the earlier 1920s, Whitehead held that there was continuity of events such that every event contained other events and was itself a part of larger events (cf. e.g., CN 59 and 76). In Process and Reality, Whitehead gave up this account of overlapping events in favor of a cosmology in which all events as well as physical processes were not continuous but discrete. In his new account, he continued to insist that geometry and physics were distinct, but the geometry of the world was now contingently affected by physical processes in small steps. It was clear to Whitehead that these steps were so small that there would be no difference between any prediction. of the type of theory he earlier espoused when it was quantized and a corresponding prediction of Einstein’s equations. The orbit of an electron around a nucleus conceived as a route of occasions would not significantly differ from that orbit conceived as the route of the continuous motion of the electron.2 Hence, Whitehead gave up his work on reformulating the equations of relativity theory, as well as any quest for ways in which his initial work would yield some confirmably different prediction from those of the equations of orthodox relativity theory.
However, in keeping with his insistence that geometry and physics were distinct, Whitehead maintained his opposition to the way in which relativity theory was understood. In particular, he continued his claim that the ideas of congruence and measurement as understood in the orthodox theories of relativity were not only wrong, but meaningless. Thus, in part 4 of Process and Reality, Whitehead shows that with some primitive ideas about region and about extensive connection, definitions of such entities as point, line, and straight line can be formulated by means of abstractive sets; he further shows that congruence relations can be defined and constructed, and how in terms of his account a theory of measurement can be constructed. Concerning Einstein’s account, he noted: "The modern procedure, introduced by Einstein, is a generalization of the method of ‘least action.’ It consists in considering any continuous line between any two points in the spatial-temporal continuum and seeking to express the physical properties of the field as an integral along it." However, . . . current physical theory presupposes a comparison of so-called lengths along segments, without any theory as to the basis on which this comparison is to be made" (PR 506f). Without that account, current theory contains undefined, and so meaningless, elements. Whitehead concludes: "For this reason, it would be better -- so far as explanation is concerned -- to abandon the term ‘distance’ for this integral, and to call it by some such name as ‘impetus’ suggestive of its physical import" (PR 507). In other words, the later Whitehead only reinterprets orthodox relativity theory and does not reformulate it.
In this reinterpretation, Whitehead preserved the separation between the geometrical and the physical on which he insisted in his earlier works. He characterized the cosmology of Process and Reality as one in which "the things which are temporal arise by their participation in the things which are eternal" (PR 63). The temporal and the eternal are mediated by the divine, in whose primordial valuation . . . each eternal object has a definite effective relevance to each concrescent process. Apart from such orderings, there would be a complete disjunction of eternal objects unrealized in the temporal world. Novelty would be meaningless and inconceivable" (PR 64). Those eternal objects which constitute the geometrical Whitehead designates as eternal objects of the objective species. A member of this species can "never be an element in the definiteness of a subjective form" (PR 445f). It is these geometrical features of the world which make possible a coherent account of measurement and so a coherent account of nature. However, in the cosmology of Process and Reality, in which events do not overlap but succeed one another, this order is itself derived from elsewhere; namely, the antecedent nature of God. It is in this way that God is now seen as the ultimate source of order in the world -- that order which is essential for our knowledge of nature.3
1In addition to his views about the physical features of the world, in these works Whitehead also developed the view that the very nature of entities referred to by such words as "red" and "green" depended on the uniformity of space-time. In the technical terminology of these works, Whitehead held that sense-awareness discloses facts within factors which are entities for thought. The separate distinction of an entity in thought is not a metaphysical assertion, but a method of procedure necessary for the finite expression of individual propositions. Apart from entities there could be no finite truths; they are the means by which the infinitude of irrelevance is kept out of thought. . . . Thus for thought ‘red’ is merely a definite entity, though for awareness ‘red’ has the content its individuality. The transition from ‘red’ of awareness to the ‘red’ of thought is accompanied by a definite loss of content, namely by the transition from the factor ‘red’ to the entity ‘red.’ This loss in the transition to thought is compensated by the fact that thought is communicable whereas sense-awareness is incommunicable" (CN 12f). In the Principle of Relativity, Whitehead went on to argue that one could refer to, and so know, factors such as red and green independently of other factors. He wrote: "You admit, it is said, that a factor is not itself apart from its relations to other factors. Accordingly to express any truth about one entity, you must take into account its relations to all entities. But this is beyond you" (R 22). To resolve this problem, Whitehead distinguished between contingent and essential relationships, which, he said, correspond closely to the traditional distinction between external and internal relations. But he added, "I hesitate to say how closely since a different philosophic outlook radically affects all meanings" (R 23). Green, he went on, might or might not be related to grass, but it was essentially related to the "passage of nature in the form of a structure of events" (R 25f). Since this structure was uniform, one could assert true propositions about a red spot here or on Jupiter, and for just the same reason that one could speak meaningfully about the distance from our sun to the star Sirius.
2For a more detailed statement of this point see my "Whitehead and Relativity," Philosophy of Science, 1955, 222-46; also, "In Defense of Duhem," Phi1o~ophy of Science, 1965, 287-94.
3In footnote 1, it was noted that the uniformity of the spatial-temporal was the ground whereby true assertions could be made about such data as a patch of color. In Process and Reality, Whitehead wrote: "A proposition can embody partial truth because it only demands a certain type of systematic environment, which is presupposed in its meaning. It does not refer to the universe in all its detail (PR 17). Of course, the ‘order’ of this presupposed systematic universe, like the ‘order’ of space-time is derived from God.